Entanglement witnessing and quantum cryptography with nonideal ferromagnetic detectors

We investigate theoretically the use of nonideal ferromagnetic contacts as a means to detect quantum entanglement of electron spins in transport experiments. We use a designated entanglement witness and find a minimal spin polarization of eta > 1/root 3 approximate to 58% required to demonstrate spin entanglement. This is significantly less stringent than the ubiquitous tests of Bell's inequality with eta > 1/(4)root 2 approximate to 84%. In addition, we discuss the impact of decoherence and noise on entanglement detection and apply the presented framework to a simple quantum cryptography protocol. Our results are directly applicable to a large variety of experiments.